Asked whether she was familiar with the three-term New York mayor, Clinton supporter Beverly Williams, 55, said, "No, I'm not."

Bloomberg's standing with politically savvy Iowans, who are used to getting attention from presidential candidates during both the primaries and general election — underscore one of his biggest challenges if he were to make a late entrance into the race. While the prospect of Bloomberg launching a third-party presidential campaign has been speculated about for years, he's largely unknown to many Americans and would be entering the race well after his rivals started introducing themselves to voters.

"Eighty percent of us in Iowa have probably made up our minds," said Angela Lambertz, a 42-year-old from Iowa City, who attended an event Saturday for Bernie Sanders, the Vermont senator and Democratic presidential candidate.

Bloomberg, a longtime Democrat who became a Republican, then switched to independent, is said to be strongly considering a bid if the general election becomes a contest between Sanders and Donald Trump.

Among Iowa voters attending campaign events Saturday, there were few Bloomberg fans.

"The communist? The anti-2nd Amendment mayor?" asked Claudia Springer, 63, of Bloomfield, Iowa, who was attending a rally for Texas Sen. Ted Cruz, a leading candidate in the Republican race.

Among those who identify with the Democratic race, Jeff Mussman, 59, of Camanche, Iowa, said he was aware of Bloomberg's post-mayoral efforts to promote tighter gun control laws, an effort he opposes.

"You can live in a big city and yeah, you might have to have gun control, but we're living here in the country," said Mussman, who plans to vote either for Clinton or Sanders (despite their support for stricter gun laws).

Bloomberg took hits from small-government conservatives when he tried to ban sales of sugary drinks larger than 16 ounces. Former Alaska Gov. Sarah Palin mocked him at a conservative forum in 2013, taking the stage with a "Big Gulp" soda.

"He's the Big Gulp guy," said Garren Bugh, 42, of Ankeny, Iowa, who also attended the Cruz event. "He's all about, 'I know better than you do.' It's the antithesis of America when we get down to micromanaging what people are drinking."